At the one-loop level, the finite-temperature contributions to the effective potential are given by [1]}, [2]}
\(V_{\mathrm {T}}(h,s,T)=&\frac{T^{4}}{2 \pi ^{2}} \sum _{i} N_{i} J_{B,F}\left(M_{i}^{2}(h,s,T) / T^{2}\right),\\\mbox{where}~~&J_{B,F}\left(z^{2}\right)=\int _{0}^{\infty } d x x^{2} \ln \left(1\mp e^{-\sqrt{x^{2}+z^{2}}}\right),\) 
